This archive is constructed to serve for references of
Random Number Generators on Computers
このアーカイブは新しい教科書
コンピュータで生成する優れた乱数とは何か
の参考文献のためにも構成されています。文献が英語の場合
短いコメントも英語で御容赦下さい。全体は未だ構築中です。
 [Download]ea4e.pdf (73KBytes)
Random Number Generator on Computers with Moduluses Formed by Two Odd and Corprime Submoduluses
Naoya Nakazawa and Hiroshi Nakazawa
(May 28, 2024)
An invention is disclosed on a class of multiplicative congruential (MC) random number generators with moduluses formed by two mutually coprime submoduluses. The generator gives MC sequences with usable periods of 2**54 or larger. Yet they admit very fast computing, by a way of decomposition given by Sunzi theorem. The present invention is concerned with cases of very large moduluses, and magical Sunzi theorem shows its own novel facet. In the presented method the MC random number generators use only the arithmetic of double precision integers (not exceeding 2**64) and double precision reals, yet respecting the reproducibility and the transportability of generated random numbers.
|
|
|
|
|
[Download]fishmanmoorenaorev.pdf (86KBytes)
Revisit to the Mersenne Prime Modulus
of Fishman and Moore
Naoya Nakazawa and Hiroshi Nakazawa
(September 13, 2015)
The report discusses exclusively on the Mersenne prime modulus d=231-1 and examines its all MC primitive root multipliers with spectral tests in regular simplex criterions. Multipliers, which were evaluated excellent in previous tests, all fail in new regular simplex criterions. A new excellent primitive root multiplier was found, but at present we find that this fails in the more stringent largest and smallest edge tests. Concludingly, the modulus d=231-1 cannot have an excellent generator in the present level.
|
|
|
|
|
[Download]
invention1a.pdf (406KBytes)
Constructive Design of Uniform and
Independent Random Number Generators
Naoya Nakazawa and Hiroshi Nakazawa
(August 6, 2014)
The report gives first the invention of extended 2nd degree spectral tests for the MC generators (d, zk) with k=1, 2, …. If the Mc random number sequence is {r0, r1, r2, … :}, the test gives us the lightest, swiftest and sharpest tool to sieve off unqualified MC sequences, if only rj and rj+k look correlated. Tests for excellent MC generators should always start from these, say for k=1, 2, … 5, at least. The method was granted Patents in RUPO and USPO. As declared in the textbook Random Number Generators on Computers, this powerful method is made open for free use to people in the world. Inventors would express their grateful regards to Patent Examiners of Nations.
|
|
|
|
|
[Download]
invention2k.pdf (356KBytes)
Method of Spectral Tests of Multiplicative Congruential Random Number Generators
Naoya Nakazawa and Hiroshi Nakazawa
(June 5-July 30, 2014)
This is the report that describes spectral tests of MC generators in regular simplex criterions, the invention patented in EPO and RUPO, Our textbook
Random Number Generators on Computers
gives a more refined introduction to this technology, preparing for developments to the longest and the shortest edge tests, which resolved problems haunted regular simplex criterions long.
|
|
|
|
|
[Download]
3978erv.pdf (3,586KBytes)
Designs of uniform and independent random numbers with long period and high precision
Hiroshi Nakazawa and Naoya Nakazawa
(March 9-July 8, 2008)
Looking back from the present, the title of this report is a misnomer and the description is circuitous. Yet, the report
gives two significant points in our knowlege which were new
at the time of publication:
(1) All random number sequences are approximated closely by MC sequences on computers, and
(2) the composite modulus should be constructed only by odd primes, without including any powers of 2.
The point (2) implies that any power of 10, for example, should not be used as modulus in MC generators. This will be detailed again in the coming extended version of
Random Number Generators on Computers.
|
|
|
|
|
[Download]
rans1203.pdf (1,198KBytes)
一様乱数の数理
中澤 宏
これは1995年頃に詫間電波高専の5年生(大学2年級)の応用数学教科書として著わしたものの復元です。当時中澤 宏は『コンピュータ上の乱数』の勉強を始めて数年、はっきり言えば『何が本質か』に理解が行き届いていませんでした。しかしたちまちこの問題の数理の魅力にとりつかれ、当たるを幸い勉強した記憶があります。この本の刊行後、『何でも、余計な事まで、書いてある』と専門家の御批評を受けたました。その通りで、何が本質と判明するかわからない、と可能な限りすべてを盛り込もうしていました。
現2021年、公開される小冊子『コンピュータで生成する優れた乱数とは何か』は、中澤 直也と始めた2008年頃の共同研究で得た3978erv.pdfの理解、『乗算合同法乱数がコンピュータ上の任意の有限長一様乱数を近似できる』から開かれた直線的諸知見を述べています。多くの不分明はここでは削ぎ落とされ、無駄のない記述展開が可能となりました。20世紀乱数理論を離れて『検定』が正確に把握されたのです。『一様乱数の数理』は現在では資料の価値しかありませんが、20世紀の代表的諸理論を正確に伝えています。そして触れられた諸テーマは面白いと感じて頂けるでしょう。御笑読頂けば幸いです。なお当時は著者にTeXに図を張り込む技術がなく、糊と鋏の作業となりました。それらの図はこのpdfファイルでは空白のままです。しかし御読みになる上では障害は少ないでしょう。
|
|
|
|
|
[Download]
jb5index.pdf (20KBytes)
jb5index.pdf
中澤 直也/ 中澤 宏
新しい日本語教科書『I>コンピュータが生成する優れた乱数とは何か』の校了原稿のファイル名を簡略化してjb521sept18.htmlとしました。その目次だけをpdfファイルとしたものをここにdownloadableなpdfファイルとして置きます。約80ページの記述内容を御覧いただけます。
|
|
|
|
|
[Download]
eb5index.pdf (20KBytes)
eb5index.pdf
Hiroshi Nakazawa/ Naoya Nakazawa
This is the pdf file of the planned Index of the English textbook Random Number Generators on Computers.
|
|
|
|
|
The rest of this archive is under the process of construction. Please kindly wait for some time.
| |